The present invention relates to a method and a device for controlling a movement of a movable machine element of a machine tool or production machine with at least two drive axles.
Nothing in the following discussion of the state of the art is to be construed as an admission of prior art.
A mechanical system capable of oscillations (for example, a drive axle of a machine tool or production machine) is typically characterized by at least one characteristic frequency that can be excited during a movement and can adversely affect the actual position value of, for example, a machine element. Excitations the mechanical system of the machine should therefore be prevented.
FIG. 1 shows in form of a block diagram a prior art electric drive system of a machine tool or production machine, which is depicted as a two-axle machine and includes a controller 1 controlling the two drive axles 6a and 6b of the machine. The drive axle 6a includes a converter 3a, a drive motor 4a and a mechanical system 5a connected with the drive motor 4a. The drive axle 6b includes a converter 3b, a drive motor 4b and a mechanical system 5b connected with the drive motor 4b. Each drive axle has a separate control unit 2a and 2b, respectively, with the controller 1 supplying to each of the control units 2a and 2b a separate desired velocity curve in the form of a corresponding desired load rotation speed nLsoll1 and nLsoll2, which represent a desired movement path of a machine element driven by the drive axles 6a and 6b. Each of the control units 2a and 2b regulates via the associated converter 3a, 3b the corresponding actual load rotation speed nList1 and nList2 according to the desired parameters set by the controller, thereby moving the machine element along the predetermined path by way of the mechanical system 5a, 5b connected to the corresponding drive motor 4a, 4b. The term actual load rotation speed nList1 and nList2 is to be understood as a rotation speed of a spindle driven via a gear, whereby, for example, during each revolution of the spindle a machine element, such as a tool, is moved along an axle of the machine by a predetermined distance so as to change the position of the machine element. The machine element is then moved on the movement path along the two axes of the machine according to the actual position values XList1 and XList2. The feedback of the actual regulated valuables required for closed-loop control is not essential for an understanding of the invention and therefore omitted from FIG. 1 for sake of clarity.
FIG. 15 shows an exemplary movement path S for the two-axle machine of FIG. 1, wherein a machine element 8 implemented as a milling cutter is guided on the movement path S. The drive axle 6a in FIG. 1 is effects the movement in the X1 direction, whereas the drive axle 6b effects the movement in the X2 direction.
The excitation of oscillations, in particular of the mechanical components of the drive axles, can be suppressed by employing a so-called jerk-limiter. In this way, the load carried by the individual drive axles of the machine can be reduced, without adversely affecting the program processing time. A jerk-limiter can be used to control the acceleration buildup of a moving machine element, thereby smoothing the desired value so that the mechanical components move with a minimum of oscillations. The term jerk is to be understood as the time-derivative of the acceleration.
In conventional machines, the jerk and the acceleration values are adapted in the controller according to the defined machine data. Because the jerk and the acceleration values are controlled along the movement path S of the machine element, there exist only a limited number of options for preventing excitation of oscillations, in particular excitation at the respective characteristic frequency of geometrically linked drive axles.
The present invention has its foundation in the method known as “Input Shaping”, which surmises that an oscillation excitation in a drive axle in response to an input impulse can be compensated by a delayed input impulse with a different amplitude. The mechanical components 5a or 5b of the drive axles 6a and 6b can be implemented by way of a so-called second-order proportional delay unit (hereinafter abbreviated as “PT2-unit”), which can be described, for example, for the drive axle 6a by the differential equation
                                                                        ⅆ                2                            ⁢                              n                List1                                                    ⅆ                              t                2                                              =                                                    ω                0                2                            ·                              n                Lsoll1                                      -                                          ω                0                2                            ·                              n                List1                                      -                                          2                ·                D                ·                                  ω                  0                                ·                                                      ⅆ                                          n                      List1                                                                            ⅆ                    t                                                              ⁢                                                          ⁢              with                                      ⁢                                  ⁢                              ω            0                    =                      2            ⁢                          π              ·                                                f                  0                                .                                                                        (        1        )            
In an ideal situation, the transmission characteristics of the controller 2a and of the converter 3a can be neglected. The following terminology is used in equation (1):    D: damping factor of the mechanical components    ω0: characteristic angular velocity of the undamped mechanical components    t: time    f0=characteristic frequency of the undamped mechanical components.
The impulse response of the PT2-unit can then be derived based on the equation (1) as follows:
                              n          List1                =                                                            ω                0                                                              1                  -                                      D                    2                                                                        ·                          ⅇ                                                -                  D                                ⁢                                                                  ⁢                                  ω                  0                                ⁢                t                                      ·                          sin              ⁡                              (                                                      ω                    d                                    ·                  t                                )                                              ⁢                                          ⁢          with                                    (        2        )                                          ω          d                =                              2            ⁢                          π              ·                              f                d                                              =                                    ω              0                        ·                                          1                +                                  D                  2                                                                                        (        3        )                                          T          d                =                  1                      f            d                                              (        4        )            wherein    fd: characteristic frequency of the damped mechanical system    Td: oscillation period length of the damped mechanical system.
FIG. 2 shows an exemplary curve of the time-dependence of the actual load rotation speed nList1 (impulse response) of the drive axle 6a according to FIG. 1 after excitation with an impulse for a damping factor of D<1. The conventional method of “Input Shaping” is used to suppress oscillations in the actual load rotation speed nList1 by exciting the PT2-unit with a second impulse which is applied with a time delay of half a period length of the oscillation period Td. The amplitude of the second impulse is selected so that the maximum of the second impulse response produced by this impulse is identical to the minimum of the first impulse response.
FIG. 3 shows the impulse response nList1 and the delayed impulse response nList1v.
FIG. 4 shows the summed impulse response of the PT2-unit from both impulses in the form of a summed actual load rotation speed nList1s. The mechanical system with the PT2-unit has an ideal transient response as a result of the addition of the two impulse responses nList1 and nList1v.
The position XList1 of the machine element along the movement path illustrated in FIG. 5 is obtained by integrating the summed actual load rotation speed nList1s. The position XList1 is normalized in FIG. 1 to a value of “1”. As shown in FIG. 5, the machine element can be controlled in the afore-described manner so as to attain a predetermined desired position without exciting oscillations. The two amplitudes A1 and A2 of the two excitation impulses can be computed as follows from the requirement that the impulse responses cancel out and the steady-state amplification is “1”:
                                          A            1                                A            2                          =                              ⅇ                                          π                ⁢                                                                  ⁢                D                                                              1                  -                                      D                    2                                                                                ⁢                                          ⁢          and                                    (        5        )                                                      A            1                    +                      A            2                          =        1.                            (        6        )            
In a practical application of “Input Shaping,” the curve of the desired load rotation speed nLsoll1 of the drive axle 6a is composed of a series of time-discrete impulses having constant amplitudes during the sampling time Ts. Because the system is linear, the relationships governing cancellation and steady-state amplification can be superimposed independently for all impulses.
This situation is illustrated in the example depicted in FIG. 6 for a step-like change in the desired load rotation speed nLsoll1 to a value of “1”. In order to change, for example, the actual load rotation speed nList1 to a normalized value of “1”, an infinite number of impulses (indicated by 3 dots in FIG. 6), i.e., an infinite number (sampled values) of the desired load rotation speed nLsoll1 of length Ts and amplitude A1 are required, as well as an infinite number of impulses with an amplitude A2 that are delayed by the delayed time Tver1 (also indicated by 3 dots in FIG. 6). Only five values are shown FIG. 6 for sake of clarity. The desired load rotation speed nLsoll1 is obtained by summing all impulses, as shown in FIG. 6 by a wider solid line. The delay time Tver1 is defined by the equation (7):
                              T          ver1                =                                            T              d                        2                    .                                    (        7        )            
When the afore-described method of “Input Shaping” is applied to machine tools or production machines with geometrically linked drive axles that have different mechanical characteristic frequencies, which is practically always the case, then the problem illustrated in FIG. 7 arises.
The movement path S illustrated in FIG. 7 is circular, with XList1 and XList2 representing the corresponding actual position values of the associated drive axles 6a and 6b. Curve 9a shows an ideal circular path, whereas curve 10a shows a somewhat distorted “circular” path when the machine is operated without “Input Shaping” and inaccuracies are introduced by mechanical oscillations of the drive axles 6a and 6b. When the machine is operated with “Input Shaping”, the curve 11a assumes an elliptical shape instead of the ideal circular shape. Although mechanical oscillations are no longer excited with “Input Shaping,” the result is not noticeably improved over a conventional operation without “Input Shaping.”
The underlying cause for this problem was unclear to this date, and the method of “Input Shaping” was therefore applied only to movements along a single machine axle, when only one axle is driven at a time during operation. “Input Shaping” and other related methods have not been applied to movements along a circular path or in two-dimensional or three-dimensional space, where the individual drive axles are geometrically linked and are operated simultaneously.
It would therefore be desirable and advantageous to provide an improved method and device for controlling the movement of a movable machine element of a machine tool or production machine with at least two drive axles, which obviates prior art shortcomings and is able to specifically operate multiple geometrically linked drive axles of these machines.